Polynomials: Factoring

5
5.1 Introduction to Factoring 5.2 Factoring Trinomials of the Type x 2 bx c 5.3 Factoring ax 2 bx c, a 1: The FOIL Method 5.4 Factoring ax 2 bx c, a 1: The ac-Method 5.5 Factoring Trinomial Squares and Differences of Squares 5.6 Factoring Sums or Differences of Cubes 5.7 Factoring: A General Strategy 5.8 Solving Quadratic Equations by Factoring 5.9 Applications of Quadratic Equations

Real-World Application
An outdoor-education ropes course includes a 25-ft cable that slopes downward from a height of 37 ft to a height of 30 ft. How far is it between the trees that the cable connects?
This problem appears as Example 5 in Section 5.9.

ISBN:0-536-47742-6

Objectives
Find the greatest common factor, the GCF, of monomials. Factor polynomials when the terms have a common factor, factoring out the greatest common factor. Factor certain expressions with four terms using factoring by grouping.

5.1

INTRODUCTION TO FACTORING

We introduce factoring with a review of factoring natural numbers. Consider the product 15 3 5. We say that 3 and 5 are factors of 15 and that 3 5 is a factorization of 15. Since 15 15 1, we also know that 15 and 1 are factors of 15 and that 15 1 is a factorization of 15.

Finding the Greatest Common Factor
The numbers 20 and 30 have several factors in common, among them 2 and 5. The greatest of the common factors is called the greatest common factor, GCF. One way to find the GCF is by making a list of factors of each number. List all the factors of 20: 1, 2, 4, 5, 10, and 20. List all the factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30. Now list the numbers common to both lists, the common factors: 1, 2, 5, and 10. Then the greatest common factor, the GCF, is 10, the largest number in the common list. The preceding procedure gives... [continues]

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